Geometric analysis of traveling wave solutions for the generalized KP-MEW-Burgers equation

Abstract

The traveling wave solution of the generalized KP-MEW-Burgers equation is analyzed qualitatively in this paper. The equilibrium properties, including hypercritical pitchfork bifurcation and transcritical bifurcation of the planar system, are analyzed in detail in the full parameter space. The global structures of the traveling wave equation are described completely. Results show that, under certain parameters, the equivalent planar system has heteroclinic orbits, homoclinic orbits, and periodic orbits. The generalized KP-MEW-Burgers equation has solitary waves, periodic waves, kink waves, and anti-kink waves. Based on the Kosambi-Cartan-Chern (KCC) theory, Jacobi stability of the discussed equation also is explored. Results show Jacobi stability and Lyapunov stability of traveling wave solutions are not entirely consistent. Last but not least, the six dimensional nonlinear system transformed from the planar system with periodic disturbance is also discussed, including periodic, quasi-periodic, and chaotic behaviors.